What is the domain of f(x)=(((x+5))/((4x^2-x-5))) ?

The domain of f(x)=(((x+5))/((4x^2-x-5))) is x 5/4

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domain of f(x)=(((x+5))/((4x^2-x-5)))

domain

x < - 1 or - 1 < x < \frac{5}{4} or x > \frac{5}{4}

Interval Notation

(- \infty, - 1) \cup (- 1, \frac{5}{4}) \cup (\frac{5}{4}, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{5}{4}, x = - 1

The function domain

x < - 1 or - 1 < x < \frac{5}{4} or x > \frac{5}{4}

What is the domain of f(x)=(((x+5))/((4x^2-x-5))) ?
The domain of f(x)=(((x+5))/((4x^2-x-5))) is x<-1\lor-1<x< 5/4 \lor x> 5/4